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Mathematics

Grade6

Easy

Question

A rectangular sheet of paper is $15 fraction numerator 3 over denominator 4 end fraction$ cm long having perimeter $56 fraction numerator 1 over denominator 2 end fraction$ cm, then find the its width.

$11 \frac{1}{2}$
$12 \frac{1}{2}$
$12 \frac{1}{4}$
$14 \frac{1}{2}$

hint Hint:

To find the width of the rectangle when perimeter and length is given use the formula ,
Perimeter = 2( length +breadth ) and substitute the given values and find the Width of the rectangular sheet.

The correct answer is: $12 fraction numerator 1 over denominator 2 end fraction$

Length of a rectangular sheet $equals 15 fraction numerator 3 over denominator 4 end fraction c m$
The perimeter of the sheet $equals 56 fraction numerator 1 over denominator 2 end fraction$ cm
Let the width of the sheet be x cm.
Then $2 open parentheses 15 fraction numerator 3 over denominator 4 end fraction plus x close parentheses equals 56 fraction numerator 1 over denominator 2 end fraction$
Converting into improper fraction to simplify the equation.
Improper fraction = $fraction numerator open parentheses text Whole number × Denominator end text close parentheses text + Numerator end text over denominator text Denominator end text end fraction$
$rightwards double arrow 15 fraction numerator 3 over denominator 4 end fraction plus x equals fraction numerator 56 fraction numerator 1 over denominator 2 end fraction over denominator 2 end fraction equals fraction numerator 113 over denominator 4 end fraction$
$therefore x equals fraction numerator 113 over denominator 4 end fraction minus 15 fraction numerator 3 over denominator 4 end fraction equals fraction numerator 113 over denominator 4 end fraction minus fraction numerator 63 over denominator 4 end fraction equals fraction numerator 25 over denominator 2 end fraction equals 12 fraction numerator 1 over denominator 2 end fraction c m$
$therefore$ Width of the sheet $equals 12 fraction numerator 1 over denominator 2 end fraction c m$

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